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The equations and theorems were sand scribbles written in the beach by Anne Schilling’s father, a physicist who worked at the European Organization for Nuclear Research (CERN). As her father wrote, Schilling absorbed as much of the information as possible before the Atlantic Ocean’s waves washed the mathematics away, the seafoam acting like an eraser on a blackboard.

On a Sunday morning in September 2023, UC Davis mathematician Roger Casals Gutiérrez was entranced by something he saw in his kitchen.

As sunlight filtered through the kitchen window, it cast its rays in a beautiful pattern on the wall. Comprised of lines, curves and points of varying illumination, the projected pattern appeared both circular and triangular, a hodgepodge of intersecting, nebulous shapes with various spots of brightness.

During the 2023-2024 academic year, my second year as chair, I focused on getting the new degree requirements approved and on adapting the Group to the new budgetary challenges that the University is facing. 

A tensor is a multi-way array of numbers. An order-1 tensor is just a vector $u \in \mathbb{R}^n$. An order-2 tensor is a matrix $M \in \mathbb{R}^{n_1 \times n_2}$. An order-3 tensor is a 3-way array $T \in \mathbb{R}^{n_1 \times n_2 \times n_3}$, and so on.

Melissa Sherman-Bennett does research in algebraic combinatorics, focusing recently on cluster algebras, total positivity, and connections to particle physics. She received her Ph.D. in 2021 from UC Berkeley, under Lauren Williams. Before coming to Davis, she was a President’s Postdoctoral Fellow at UCLA and NSF Postdoctoral Fellow at Michigan and MIT.

Abi Gopal joined the Department of Mathematics in July 2024 as an assistant professor. Prior to this, he was a Gibbs assistant professor of mathematics at Yale University.

Abi's research is in the field of numerical analysis. He is particularly interested in numerical methods for integral equations, analysis-based algorithms, and numerical linear algebra. His work is primarily motivated by applications in wave propagation and quantum chemistry.

Informally, a mechanical linkage is a system of rigid links (rods or bars) connected by ideal joints and moving in the plane or in the space. This definition suffices for engineering purposes, and one can find it in some form in many engineering books. However, from the mathematical viewpoint, this is not a satisfactory definition.

After earning her B.S. in Mathematics in 1966,  Joan Marie Peters Ogden was a GS-7 mathematician in the Ships' Engineering section in the U.S. Navy in 1966 and 1967. While there, she helped NASA with mathematic modeling for naval ships, modeling ships motions to drive the hydraulics necesary for keeping the communication dish steady, to keep the dishes trained correctly during the Apollo Program.

I spent 10 wonderful years at Davis, completing both my B.S. and Ph.D. in the Department. During my final year of grad school, I interned as a Pathways intern at NASA’s Ames Research Center, and after completing my Ph.D. in 2021, joined NASA as a full time research scientist. 

Melissa Zhang is a low-dimensional topologist who likes to use algebraic, combinatorial, and categorical methods to solve problems. Her favorite topological objects are knots and surfaces smoothly embedded in 3- and 4-dimensional spaces.

She received her Ph.D. from Boston College under the supervision of Eli Grigsby and David Treumann. She was previously a postdoc at the University of Georgia, SLMath/MSRI, and UC Davis (and is now a super-postdoc, as she never left).

We are welcoming 11 new graduate students to the Mathematics Ph.D. program this year, and we have 75 Ph.D. students in total in the program. Last year, 11 of our students completed their Ph.D.’s and have continued their journeys in careers in academia and industry.

This also is the start of my second year as vice chair of graduate affairs. Over the last year, I have tried to approach challenges with empathy and a problem solving mentality. Here are some of the initiatives and challenges from the past year.

After graduating from UC Davis, I went on to obtain a Ph.D. in Economics from Harvard in 1983. I taught for six years as an assistant professor at UC Irvine before moving to Dickinson College in Pennsylvania, where I still teach. Being at a liberal arts college has allowed me to stretch beyond my formal area of expertise. I have done that extensively, working in areas as far-flung as sports psychology, political geography, communications theory, public health, economics pedagogy, as well as a bit of economics. 

Our undergraduate math programs are thriving! Last Winter, undergraduate programs underwent its seven-year Program Review. The external reviewers described our Department “to be dynamic, welcoming and a great place to study Mathematics” and said that our program’s strength was centered around “committed faculty, lecturers, staff and TA’s that come together to deliver a strong program to incoming students through to graduate education.”

This past academic year, the Department awarded 184 degrees!  

With the anticipation of Data Science activities in full swing at UC Davis, in Fall 2020, our campus decided to renovate the first floor and basement of the former Physical Sciences and Engineering Library (PSEL) for the use of campus-wide Data Science and Artificial Intelligence (AI) related activities. The renovation was finally completed in December 2023.